Take the motorway A2 direction Wien (Vienna), the first exit Graz-Ost and then the third exit at the mall „Einkaufszentrum Murpark“. Take the first exit in second roundabout. You’ll find the Römerstube after about 200 m (220 yards) on the left.

Via taxi:
The costs of a taxi ride from Flughafen Graz – Thalerhof to the Römerstube range from € 12 – € 15 depending on time of the day and traffic.